Yes you should go for next round. As REC MAINPURI is a college which is established few year before.

RajkiyaEngineering College is a reputed engineering university under government ownership.

REC Mainpuri was established in 2015 whereas REC Bijnor was established in 2009. You can come to know about these Colleges by visiting their respective websites.
You should go for REC Bijnor, even though the fees is a little higher compared to REC Mainpuri. So do according to your rank also.
REC Bijnor was established earlier so it has some established reputation and we know that the faculty are highly experienced and  good campus life here.
Placements record is there although not highly impressive but some companies do come, but because REC Mainpuri was recently established there is no record of placements yet even though they say they are working on it.
Consider the above information.