A typical "small" transaction on Monero is about 400 bytes. Here's a recent small transaction (2 inputs, 3 outputs)

http://monerochain.info/tx/4433b7a5813428fe96111a2f7b9b9af5a1b10f153d9a8c18c1ff391c8993c266

A typical "small" transaction on Bitcoin is about 400 bytes. Here's a recent small transaction (2 inputs, 2 outputs)

https://blockchain.info/tx/081d5317f0885523c30b5035b1662776ab60f148d4525ccf0531be65ddc8db10

Obviously there are a range of transaction sizes on both networks, but there is no exponential increase. None.