I know you can't really say that a non-digital format such as VHS and Betacam (or LP for sound) have a resolution but it should be possible to give an rule-of-thumb estimate, shouldn't it?
Wikipedia gives some number (300 for Beta and 340 for Beta SP) but that sounds too low doesn't it? PAL and NTSC are 575 and 625 lines and Beta (SP) was used for that, wasn't it? Why this discrepancy?
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The resolution is correct, but your understanding of how that is measured is confused.
Analog video consisted of a series of continuous horizontal lines. Don't confuse the number of vertical lines with "lines" of horizontal resolution. When you talk about horizontal resolution in terms of "lines" you're actually talking about how many line pairs—or literally how many vertical black and white lines—the format could possibly reproduce. To compare it to pixels, consider that it takes two lines of pixels to reproduce a line pair: one line of black pixels and one of white pixels. So double the analogue measurement to get the digital comparison.
So while line pairs is the measurement used for the horizontal resolution, the vertical resolution is locked to the television standard, 576 lines for pal, and 480 lines for NTSC.
The horizontal resolution can be calculated from the bandwidth using the rule of thumb for resolution of 80 lines per MHz of luminance* bandwidth. Betacam had a bandwidth of 4.0-4.5 MHz, which works out at 320-360 lines. This equates to 640-720 pixels of resolution, or roughly the same as DV.
TL;DR: Betacam's resolution was roughly equivalent to 720x576 for PAL, 720x480 for NTSC
*luminance had higher bandwidth than chroma, just as digital formats subsample the chroma information, usually at half or even quarter resolution.
