First off I have over 400 hours between both games so feel I have some merit when it comes to making suggestions to others about them. This review is to help people who don't know whether to start with Galleria or Refrain. I've played both and have some insight that may help you make that decision. Which you choose largely doesn't matter if you just want a super fun, grindy, turn based dungeon crawler. Both games are equally fun in that regard. In fact I'd go so far as to say they are my two favourite dungeon crawlers bar none. Where they differ is mostly in small QOL differences and level design. It is a matter of personal preference, though mine may help you decide if you choose one or the other.

I'll start with Labyrinth design as that is the majority of the game. Refrain's labyrinth is more enjoyable to explore for several reasons. The first being it was less confusing initially. During the first and second map sets of Refrain I got confused and lost far fewer times than I did when doing the first two maps of Galleria. Galleria's first set of maps seem purposefully obtuse to stump players and artificially inflate play times, where as Refrain's first set of maps are pretty easy to figure out and keep you engaged for longer, giving you time to bond with the characters and world without getting frustrated immediately.
Artistically, the design of the backgrounds, textures, environments, breakable objects and chests in Refrain all scream creativity and quality. Galleria is nicely designed as well, but I found the areas very "samey", particularly in the infamous second half of Galleria. Refrain does not suffer from this problem with back to back environments being wildly different. Galleria is also more vertically challenging ie going up and down stairs to get around blockages and unlock secrets, where as Refrain's maps seem larger and more spread out with fewer stairwells and pit falls.

Galleria's Labyrinth rating = 8
Refrain's Labyrinth rating = 9.5

The differences in quality of level design between the two games are barely discernible, but they are there and IMO Refrain is the clear winner.
Refrain's maps are, overall, more engaging to interact with (particularly from an ADHD player perspective) ie finding little holes in the walls to crawl into to escape enemies or find loot, or needing to speak to a ferryman to help get you across the swamp map. These instances are small but numerous and add up to a labyrinth I feel has more charm. Galleria's maps have their own charms and oddities as well don't get me wrong and I enjoyed the hell out of the game no question, Galleria just isn't as weirdly satisfying as Refrain is to play for me.

Switches/Buttons are another place I feel Refrain excels. Their designs are more varied from map to map than Galleria's and visually indicate their "status" (ie activated/not activated) better. A pull chain that has been pulled down and has changed color indicates that that "button" has been activated far better than the barely perceptible change in depth of the buttons you are working with in Galleria. I do like that Galleria indicates with a flashing circle which door the button unlocked, an improvement over Refrain which does not provide this secondary visual indicator for buttons/locked doors.

These games do take place in the same world, though they are barely connected. There are subtle nods in each to the other but that is it and you really have to be involved in the story and world lore to even notice them anyway. I will say the story elements are way more enjoyable in Galleria; the concept the excecution and the characters are all much more interesting and fun to learn about. I prefer the characters in Galleria more than in Refrain for sure, though Dronya, Luca, Mareietta, Neldo and the rest all have their unique...charms...
The voice acting is good in both games so that's a big plus! Both games have a horror undertone to them and in Galleria a few things happen near the end of the first half that did shock me a bit, though I won't spoil them here. Not that it matters much but in case this floats your boat, both games have Yuri/lesbian undertones and light sexual situations that are cute/funny when they appear. These elements were largely toned down in the translation of Refrain but Galleria's translation seems to be pretty faithful to the original.

Female main characters are the name of both games really and in case you were wondering both games pass the Bechdel test with flying colors. Though I use female pronouns I seldom enjoy all female or primarily female casts in things, with these games being a major exception. I adore all the characters, good and bad ones, in this franchise and I'll leave it at at.

Sound effects carry over from Refrain to Galleria with a few small exceptions that aren't very noticeable, though when it comes to music I prefer Galleria's. As an ASMR fan, I found turning all the music off and just walking around in the labyrinth was satisfying to my ears as the footstep sound effect is *chef's kiss*

The combat systems work nearly the same in both games! One noticeable difference in combat between the two games is Refrain's lack of enemy health bars. Galleria has health bars however lists them as "unknown" until you've defeated that enemy type at least once. As the first game in the series Refrain does an excellent job gradually introducing game mechanics to the player, both in tutorial pop-ups and in the story itself. Galleria does this also, just to a lesser degree story-wise, relying more heavily on one time pop-ups you are free to read later if you are confused. The learning curve in Refrain is far gentler to the player then in Galleria, though that makes sense given Galleria is the 2nd instalment in a series with mechanics upon mechanics upon mechanics. There is a certain level of presumptuousness in Galleria that the player is familiar with all of them from the first game. As Galleria was actually my introduction to the series, not Refrain, perhaps my view is a bit skewed as I went in without prior knowledge of the series and found it to be a bit steep in terms of learning curve. I was comparing it at the time to other games in the genre like Undernauts: Labyrinth of Yomi rather than Refrain.

One area Galleria has Refrain beat is in puppet creation/unit creation. There are simply more options and little things you can tweak such as color that help make each soldier you create unique. It's not a big deal until you get into the later game, but in Refrain I found I was making essentially duplicate puppets with different names to fill out my covens as I had already used all the soldier designs (each facet/soldier type only has 3 maybe 4 portrait options where Galleria gives you this, plus additional color options within those initial visual options to choose from.) I'm still unsure what choosing a puppets favorite food or animal does to them overall in Galleria as it is not explained, though just like with a units lucky number, I'm sure it can affect small situational stat-based things behind the scenes.

All in all both games are incredibly addictive no matter how you look at them. I can't recommend them highly enough, especially if grinding levels to get an OP team and smashing through games like these is your preferred way to play. You can essentially auto-battle your way through normal mode, with the exception of a few boss fights you might actually need to be strategic about. For some folks this might be a turn off and for those people you are free to micro manage and plan out every battle with your units. My focus when playing has been largely to work on making covens that sync up well together and beef my units that way, strategically speaking, rather than micro manage them by issuing commands to each unit during every battle. I just like auto battle functionality in games, especially grind heavy games like this where the flow of the game essentially becomes: Dive into labyrinth, explore until you can't progress anymore due to a big boss monster in your path, proceed to grind for hours until your team can beat the boss, progress until you can't anymore due to big boss monster, rinse repeat.

For those that want to grind efficiently I have a guide available Here[gamefaqs.gamespot.com]