Ignoring ESR for a moment. I can make that work. Lets say all the options have the same 5mOhm ESR.
Is there a reason an MLCC or Tant or Ceramic all of equal values buffer the input to an LDO like an electrolytic would?
edit: I'm interested in the question right there because I'm finding it extremely difficult to find a 40V+ rated 10uF that fits in my height requirements. If I can looked at other styles it would help. Unless someone has a 3mm tall 10uF electrolytic that's cheap!
OK, as you have the capacitance value and the ESR values established for your design, here are some points about the two capacitor types that you mentioned as possible replacements for aluminum electrolytic capacitors.
Tantalum (solid)
Tantalum capacitors would make good replacements as far as capacitance and ESR are concerned. But there is one problem. Tantalum capacitors should not be used where the current is not limited to a low value, or tantalum capacitors may fail and sick their guts all over the place- that is the general view anyway. This means that tantalum capacitors would not be suitable for your application.
Ceramic
Ceramic capacitor plus points
p1) high capacitance/volume ratio
p2) low ESR
p3) long life (practically infinite, unlike aluminum electrolytics)
Ceramic capacitor minus points.
m1) capacitance very dependent on applied voltage
m2) capacitance dependent on temperature
m3) microphonic
The degree of the above minus points is highly dependent on the dialectic material of ceramic capacitors.
To short a long explanation, the only dialectics worth considering for your application is X5R or preferably X7R.
There is another catch. In general, the smaller the ceramic capacitor, the worse are minus points, m1 and m2.
You should work out all these parameters from the capacitor data sheet but, as a general rule of thumb, whatever minimum capacitance you want, chose a ceramic capacitor of twice that value, with a maximum of 15% tolerance and X7R dialectic. Furthermore, chose a ceramic capacitor to be as big as possible (not good for your application) and as higher voltage rating as possible.
There is a lot of information about ceramic capacitor characteristics from the manufacturers, but to get a quick feel for ceramic capacitors have a look at page 15 of the data sheet for the LT1763 series, LDO voltage regulators:
https://www.analog.com/media/en/technical-documentation/data-sheets/1763fh.pdfDon't let all the above put you off ceramic capacitors. They are amazing components, but you need to do a worst-case budget to ensure that a particular ceramic capacitor meets all the requirements of your application, and under all operating conditions. But, if your application needs low distortion, be very wary of ceramic capacitors!