Low-end DSP vs High-end MCU
I would like to slightly extend your question:

Low-end DSP vs High-end MCU vs Analog

and try to answer it.



High-end MCU

Modern MCUs are very powerful. The table presented below lists the results obtained performing a synthetic test consisting of two sequence of FFT and then by-element square and then dot product on a distinct 12800-point floating point array within each iteration, expressed in iteration per second done [it/s] and iteration average time [us = microseconds]:    

Device-under-test        it/s    time/it, us   Remark
TMS320C6422B             2.50        400 000
MityDSP-L138F            3.97        252 188   L3 cache off, about x7 with L3 cache on
InMys SOM-AM180X-L8      5.90        169 491   L3 cache off
VAR-SOM-OM3X            37.00         27 027
RaspberryPI             35.80         27 933
InMys SOM-AM180X-L8     52.20         19 157   L3 cache on
Renesas RZ/A1H          54.61         18 311   linux, data+code in internal sram
Colibri VF61            56.80         17 606
Intel Core i3          949.42          1 053
Intel Core i5        1 583.84            631


As you can see, modern 500+ MHz Cortex-A5 w/FPU based MCU installed in Colibri VF61 beats a dedicated floating point DSP such as C642x based 250 MHz TMS320C. And does it significantly. But of course, Core i's beat them all.



Low-end DSP

Being beaten by modern MCUs in performance, modern DSPs strike back beating MCUs in... architecture.  Generally saying, a DSP IC architecture is intended to continuous + on-line + strictly timed + isochronous data processing, i.e. it by-design has special units to regularly read-in and then process and then write-out continuously going digital data in a form of samples. Also, it can be integrated with ADCs as a original samples source and DACs as a processed samples destination, simpler and practically glue-less, again thank to dedicated "on-chip" architectural units providing dedicated interfaces. MCUs, even high-end ones, typically cannot boast in this.  



Analog filter

Both MCU and DSP are digital things. Working with digital, you need to understand its limitations: quantization and grids. Using integer numbers in filters is simple but gives significant quantization noise; using floating numbers in filters is flexible but gives implicit exceptions like a surprising NaN in continuous accumulation killing the filter off. Analog is alternative for that.

Maybe analog looks like something from the past, but it never looks like something useless, even today. Natural effects taking place in a lamp or semiconductor cannot be ideally modeled in MCU/DSP, maybe only in a supercomputer cluster but then not in a real time :-)

Making a choice between designing digital or analog, ask yourself what do you really and exactly want: to control or to enjoy? If to control, take digital, if to enjoy, be bolder with analog.