Replacing RAMPS 1.4 for 1.6
RAMPS 1.6 is very similar to RAMPS 1.4. Most, if not all, of the changes are hardware improvements, without making the core functionality different. Looking at the incremental changes between versions:
To quote from RepRapWiki: RAMPS 1.5

The RAMPS 1.5 is a variation of the popular RAMPS boards that, like
all other RAMPS boards, is plugged into an Arduino Mega for operation.
The layout of the RAMPS 1.5 is virtually identical to that of the
RAMPS 1.4. The only real difference between the two are the MOSFETs
and the fuses.

To quote from RepRapWiki: RAMPS 1.6

The RAMPS 1.6 is the second RAMPS iteration released by
BIQU/BIGTREETECH. It replaces the original green power connector with
a pair of screw terminals, adds a larger heatsink over the MOSFETS,
and has a larger bed MOSFET. It maintains the surface-mounted fuses
and flush MOSFETS of the RAMPS 1.5.
Also, the positions of the D1 and D2 diodes have been swapped from the
positions in RAMPS 1.4, the D1 diode is now the diode closest to fuse
F2. The same is true for RAMPS 1.5, also manufactured by
BIQU/BIGTREETECH.

So, in short, yes, the RAMPS 1.6 should be a direct plug in replacement for the RAMPS 1.4.
That said, you may be able to salvage your RAMPS 1.4, if you can locate the part that has given up the &quot;magic smoke&quot;. It could just be a blown capacitor, or diode. There have been a number of questions relating to that, so it might be worth searching for answers here, on SE.3DP1.
It is probably also worth reading RAMPS 1.4, 1.5 or 1.6?

Additional links
An interesting video, where a variety of RAMPS 1.4 boards are compared, is the first of a series, RAMPS series 1 of 5 - Intro and board comparisons - although beware the loud music...
There is also a RAMPS 1.6 Plus, and a RAMPS 1.4.2 which might be worth considering. I wrote up about these, briefly, (disclosure) in my personal blog, a couple of years ago: 3D Printer control boards.

Footnote
1 Such as How drastic is reversing the polarity of the power supply to a RAMPS board?, which might be relevant in your case.