Depends on what you have to pay for the popcorn.
A popcorn A-110 will cost you 200 - 250 euros here in the Netherlands.
I came up with this list for a HTPC. Keep in mind that this is the cheap list so don't expect incredible results.
Case: NOX Media 64,-
Mobo: Gigabyte GA-73PVM-S2H 60,-
PSU: Be Quiet Pure Power 300W 35,-
Memory: Corsair CM2X2048 - 6400C5 2GB 33,-
HDD: Seagate Baracuda ST3160813AS 160GB 29,-
CPU: Intel Celeron E1200 32,-
This makes a total of 253,-
So its in the range of the popcorn but will give you more fun I think. Install Mediaportal and you have a great looking machine with more features than a popcorn and you can always upgrade it.
I would go for the HTPC, and I would up the budget to 300,- but that's just me.
Check out my custom HTPC