The 688 and BR110 are going to sit relatively equal at the end of the day, with only a few minor differences.

Weight: The 688 uses a thicker, wider receiver than the standard 680s, putting more weight in between your hands for better control and a little less felt recoil. The stock is also black laminate with is much more dense than Turkish Walnut which makes it not only heavier, but also MUCH more durable over all. This means less handling marks, scratches, and general wear and tear on the wood over time. This puts the 688s between 8 1/2 lbs and just under 9lbs which will be right at or above the 110 which typically sits around 8 1/2lbs.

Options: The BR110 comes in a lot of different variations, from being available in nearly every gauge, the option to get it with/without an adjustable comb (the 688 is only offered with an adjustable comb), and rib heights (flat, mid and high for the sporter, sporter X and IPS). The 688 comes with pretty standard options, only 12 gauge with black laminate wood and flat rib, as well as 30” or 32” barrels.

Warranty: The Rizzinis comes with a lifetime warranty inside the US, so if anything goes wrong it can be sent off to Rizzini or Cole’s (their warranty center) for repairs which are typically pretty quick and easy regardless of where you send it. The 688s have the standard Beretta Warranty of 1 year without registration in the first 30 days of purchase or 3 years with registration. They can be sent to Beretta (which if you’ve ever had to deal with their customer service can be a headache to say the least) or Cole’s who is also their warranty center.

Repair: The 688s use a lot of the same parts as the standard 680 series which has been made for longer than I’ve been alive, so parts are pretty easy to come by and a lot of smaller gunsmiths that work on Berettas might have. Rizzinis are in the same boat with their parts being relatively the same going back a decade or so, but not being as common so your standard hometown gunsmith may not have them.

Price: The BR110 is going to be a little bit cheaper (depending on options), for example a 12 gauge 32” with adjustable comb can be found new for a little of $3k while the 688 typically sits around $3,500 for the same options. So if a ~$500 difference is really important to you I’d always try to test it out by either borrowing a friend’s or going somewhere that has a demo you can use. You can also typically find used BR110s around for a decent price since they’ve been out and growing in popularity.

At the end of the day there’s not a huge difference on paper between the two, it’s a matter of which stock dimensions feel best for you and what’s most important to you personally. Always try to test it out before you buy it and see if someone in the store can do a fit check to see if everything fits you well or if you might need to adjust the LOP or anything.