I'd say the 345. It certainly costs less than a 1911 from anyone. Another thing to consider is if you carry the 1911, the best way is cocked and locked rather than having to charge the weapon when you need it. With the 345 you can carry a round loaded and the safety off and just pull the trigger if necessary. Which wasy would you feel more comfortable with? If you like the 345 way get that one and then safe up for a 1911 and use it as a range/house weapon and the 345 as a carry/range weapon.
I'm a big 1911 fan, but if you like and know the P series, nothing wrong with staying with a P. If I was in your shoes and considering a 1911, I would probably borrow or rent one and head to the range to see if it agreed with me before spending that kind of money. A 1911 is really a breed apart and, as much as I love 1911s, they don't agree with everyone.
Nothing wrong with either one - they are both reliable pistols...
However, I you're just trying to create a 'collection' then I think every 'collection' should have a 1911 in it.
BUT if you're looking for a .45ACP pistol for social work or something other the 'show and tell' then I think we've learned a few things in 100 years. For those uses I'd go with a DA/SA weapon, P345, SIG P220, SA XD, etc.
it's a tough call for anyone and nobody can tell you the wisest choice FOR YOU.