For those who don't already know, it is possible to create a DIY air filter on the cheap using a box fan + furnace filter. Is there a big difference between Merv and HEPA?
Merv stands for Minimum Efficiency Reporting Value. Higher Merv typically equates to more aggressive filtering but this can come at a cost of more expensive filters with lower air flow. Higher Merv means the filter will filter out a smaller particle size, down to 0.3 micron. Merv 13-16 has a minimum 0.3 micron particle size, and there are Merv which go as far as Merv 20 with < 0.3 micron which can even capture viruses and smoke. Generally from what I gather there isn't much benefit economically for allergy sufferers to go with anything more than Merv 13 but if you've got the money and want to you can go with Merv 20.
HEPA generally is what most standard air filters use and the HEPA filter also filters out at 0.3 micron. HEPA filters are much more expensive but at the same time seem to be slightly more effective. So they cost more, but are more effective too. Generally though the filters do not last so if you use a HEPA filter or a Merv 13 you will have to replace them but it seems the HEPA filters have to be replaced much sooner particularly because they are more likely to capture particles at a faster rate.
Conclusion
Merv 13 with a box fan seems very effective and cheap. Price to performance favors a DIY approach using a box fan and Merv 13. If you've got plenty of money and want quality well then you can go with HEPA as this can clear the air at a faster rate. Generally though they both clear the air at around the same level so there is no noticeable difference.