They are both built to do the same roles, but come at it from very different perspectives-
The sig is a rolled metal upper with the interior pinned in. The lower is alloy. Folks would claim the positive of the design is it is simple, and will take great deals of abuse. I have seen them come out of mud and fire.
The Beretta is a slug of steel machined out for a upper. Extremely machined out to the famous bare slide look. Folks say the positve of this slide is less jams and easier to clear. The lower is an alloy.
The Sig uses a series of safetys that cumulate in a passive decocking system, ready to fire with the squeeze of the trigger.
Beretta uses a series of safetys that cumulate in a on the slide decocking/lock level that would need to be released to shoot. There are tons of varations on this however, so if you look you could find a very similar setup, a decocker only device.
The extractor in the Sig in internal and protected, the beretta's is open and used as a loaded round indicator.
The Sig traces it's design back to some of the 1930 Sauer designs, and the Beretta goes back even farther to the 1920 designs.
There are some used bargins of both types out there right now due to police trade ins. Use high caps can be found at decent prices for both currently.
The Sig is easy in install night sights on, and can be found new or used with them. The berretta, well, not so simple
Personally I prefer the Sig, it fits better in the hand to me, and is a joy to shoot. The beretta is is a fine firearm, I find them a little too large and heavy for my taste.
Don't take military use as a bid say so though, except of some of the decisions in the special ops community, most final choices are made on cost factors, and what the manufacturer will provide a "sweetener" to the deal. In the case of the model 92's selection for example the final decision makers were price per unit, and the willingness to build an assembly plant i the United States. Sig could not match the price, and would not at the time turn production soley into a US based manufacturing facility.
I would suggest perhaps trying both if you can at a local range that "rents" guns. There is at least one gun local range locally for me that has a changing, wide variety of guns you can rent, so you can see which feels better to you, and which you enjoy the most.
At this rate, both are in the first tier of design, build, and manufacture- so you won't go wrong in either direction.
So if you can, try before buying.
I have owned both, in several different configurations, but of the two, I still own sigs, three, and no berettas currently.
Let us know what you decide on.