I think I can count the games I've seen someone actually react a Beggar on my fingers and I've been playing since before Dark Ages came out anyway, the below the line parts of both seem pretty irrelevant to be honest.
Different experience for me. The Reaction is far more useful than the on-play effect which isn't surprising as 2 Silvers are nearly always superior to 3 hand-gained Coppers. Gardens, Monastery and Guildhall Kingdoms with trashers are the only situations which come to mind in which you might want to play Beggar.
2 Silvers on the other hand are useful in a zillion of situations and the topdecked Silver defends against nasty trashing attacks.
Guildhall-Beggar doesn't need trashers, it just kind of buys Provinces until they empty, quickly. You can also use Beggar to gain fodder for things like Forager, or Altar or Mercenary or whatever thing that does something unique in the kingdom but needs fodder to trash.
The Beggar reaction is probably relevant with Knights sometimes, but that's about it really none of the other junking attacks are really very good. Basically for Beggars reaction to be good you need an attack in the kingdom (obviously) and you need to be getting attacked often enough that you can reliably trigger the reaction, which basically only happens in engine games and you need gaining 2 Silvers to be good enough that it's worth adding a dead card to your deck, which is rarely the case in an engine. So you really need the stars to align to have that reaction be relevant.
Here's my entry. Trade Pact is similar to Masquerade (without passing) the turn you play it, and then gains a Silver to your hand on your next turn. While it's in play, when an opponent trashes a card, you have to as well. This is of course potentially beneficial in the early, but eventually you may be forced to trash something good. The Silver gaining can mitigate your losses, while also providing trash targets later (both for "defense" or "attack"). $4 might be too cheap, but it also felt a bit weak at $5 since you only get the Masquerade effect every other turn. Feedback is appreciated!
I doubt you'll realistically ever be forced to trash something good with this, you usually just stop playing your trasher when you run out of cards to trash.