The differences between these two altars range from the obvious to the obscure. In the obvious category are all those structural details which make the Tabernacle altar portable, such as the smaller size (it measured just 5 amos to a side, as opposed to 32 amos), the hollow interior which was filled with dirt when the Jews camped and emptied during travel (as opposed to being made of solid stone), the walls being made of wooden planks plated with copper, and the need for poles to carry it.
An interesting fact about the poles is that they were placed just above the midpoint of the Altar, some 6 amos from the ground. Now, most people measure 3 amos from their shoulders to the ground (Meiri to Shabbos 92a) which would make it nearly impossible for anyone to even reach the Altar's poles, let alone carry them on their shoulders. Turns out that the Levites, who carried the Altar, stood 10 amos tall and could easily handle this job (see Shabbos 92a).
Among the more subtle differences is that the Yesod of the Tabernacle Altar went around all four sides. In the Second Temple, due to certain technical requirements which had to do with the location of the Altar with respect to the boundary between the tribes of Judah and Benjamin, there was no Yesod along most of the southern and eastern sides of the Altar. In the wilderness this was not an issue, hence the Yesod could surround the Altar on all four sides.
I assembled a Lego® model of both altars which I usually show together so that people can get a sense of the difference in size between the Tabernacle Altar (which most people are more familiar with from reading about it in the Torah) and the vastly larger altar built for the Second Temple. Below are some pictures of the Tabernacle Altar model. The body of this altar measures about 3 inches to a side and 6 inches tall.
Lego® is a trademark of the LEGO Group of companies which does not sponsor, authorize or endorse this site