You probably have 7020 sff motherboard which has no Dell backplate. The sff board is mounted to chassis studs/standoffs in sff case. The 3010 mt motherboard has Dell M3 backplate so it does not use chassis standoffs, thus mt case has no stand-off. To install sff board in mt case you could consider use generic M3 backplate for LGA115# socket such as this.

SFF case w stand-offMT case no stand-offSFF board no Dell backplateMT board w Dell backplate

Also, 7020 SFF and 3010 MT have different front I/O panels.  So I'm not sure if compatibility issues will arise.

brad has a good point.  SFF back IO shield is fixed in SFF case which means you can not move it to MT case.  I would just leave it without shield after swap.