Not a real world scenario, and FH won't do anything to help you win contest or daily high score. Also, not sure it's not the correct play- the strategy in alpax's post has a note about the 2 pair with one Wild! in deck, keeping the higher pair- but it's not clear the way it's referenced.
Holding the pair of deuces in this case does have the higher expected value (9.5404 per hand).
Holding both pair gets you 5 full houses and 43 two pair among the 48 possible 1-card draws for a slightly smaller EV of 9.1667 per hand.
Holding only the deuces is going to cause a whiff almost 2/3 of the time, but that wild card in the deck and the big pays for 4 or 5 deuces puts holding only a single pair of 2s over the top.
If you don't draw the wild card among the 3 new drawn cards, the EV is only 4.7160, but if the wild card is among your 3 new cards, the EV explodes to 81.9056 per hand.
So, with this TDB pay schedule the bare pair of deuces, although a much riskier hold, is the correct play both for the contest and if you want to maximize expected value "for real money."
The ordered pairs below are the number of possibilities when holding the pair of 2s, first when you do not draw the wild card, and second when you do.
No Win (0 coins): (11520, 0)
Two Pair (5 coins): (2629, 0)
Three of a Kind (10 coins): (1852, 926)
Full House (45 coins): (169, 64)
4 2s w/o kicker (400 coins): (33, 66)
4 2s w/ kicker (2000 coins): (12, 24)
5 2s (2000 coins): (0, 1)
Total Possibilities: (16215, 1081) for a total of 17,296